5 problems

Degtyarev's conjecture. If $g(\SS)>0$, then $\SS$ is realized by exactly two rigid isotopy classes of irreducible sextics, one abundant and one not. If $g(\SS)=0$, then $\SS$ is re…

Connectedness and abelianity conjecture. The space $\mathcal M_{nt}(6A_2;6)$ is connected, and the fundamental group

Let $C_0$ and $C_1$ be the curves and let $g_0$ and $g_1$ be the polynomial function germs associated with them. Write $V(g_j)$ for the zero locus of $g_j$ and let the monodromy of…

For $ue 3$, define the numerical invariants … … … Let $V(d,c,n)$ be the space of irreducible plane curves of degree $d$ with $c$ cusps and $n$ nodes as their only singularities, a…

Let $V(8,12,0)$ be the variety of irreducible plane curves of degree $8$ with $12$ cusps and no nodes, and let $B(8,12,0)$ be the family of degree-$8$ branch curves arising from ge…